The cell‐based method of domain decomposition was first introduced for complex 3D geometries. To further assess the method, the aim is to carry out flow simulation in rectangular ducts to compare the known analytical solutions.
The method is not based on equal subvolumes but on equal numbers of active cells. The variables of the simulation are stored in ordered 1D arrays to replace the conventional 3D arrays, and the domain decomposition of the complex 3D problems therefore becomes 1D. Finally, the 3D results can be recovered using a coordinate matrix. Through the flow simulation in the rectangular ducts how the algorithm of the domain decompositions works was illustrated clearly, and the numerical solution was compared with the exact solutions.
The cell‐based method can find the subdomain interfaces successfully. The parallelization based on the algorithm does not cause additional errors. The numerical results agree well with the exact solutions. Furthermore, the results of the parallelization show again that domains of 3D geometries can be decomposed automatically without inducing load imbalances.
Although, the approach is illustrated with lattice Boltzmann method, it is also applicable to other numerical methods in fluid dynamics and molecular dynamics.
Unlike the existing methods, the cell‐based method performs the load balance first based on the total number of fluid cells and then decomposes the domain into a number of groups (or subdomains). Thus, the task of the cell‐based method is to recover the interface rather than to balance the load as in the traditional methods. This work has examined the celled‐based method for the flow in rectangular ducts. The benchmark test confirms that the cell‐based domain decomposition is reliable and convenient in comparison with the well‐known exact solutions.
Wang, J., Zhang, X., Bengough, A.G. and Crawford, J.W. (2008), "Performance evaluation of the cell‐based algorithms for domain decomposition in flow simulation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 18 No. 5, pp. 656-672. https://doi.org/10.1108/09615530810879765Download as .RIS
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